It appears APV PDF Viewer may be abandoned. It has not been updated recently, has been removed from the Google Play Store (both the free and paid versions), and the latest version is not available on F-Droid.

Requirements

Must not require internet access. If it wants internet access at all, the reason must be disclosed.

Must be compact. The total size when installed must be under 10MB. (Note that Google Play Store seems to show the download file size, but no the size when actually installed.)

Again to fill the waiting time: PDF Stuff would be the place to look. My favorite wouldn't really match your requirements: Moon+ Reader Pro is pretty fast and convenient – but neither open-source/freeware nor that compact. But it can deal with plenty other (eBook) formats as well, and has pretty good support. If that would be an option, let me know. MuPDF however might be a perfect match for you (also available on Playstore).
– Izzy♦Apr 22 '15 at 9:49

@Izzy Thanks Izzy. MuPDF is my backup choice if no one can find software to meet the above requirements. The downside to MuPDF is the size; when installed, it is over 15MB in size. It's surprising, given that it uses the same PDF libraries as APV (namely, the MuPDF libraries).
– RockPaperLizard♦Apr 22 '15 at 19:21

So should I make that an answer then? If you already tried it, you could point out the core of your experience in a comment to that (I've not used it, so I cannot contribute experiences).
– Izzy♦Apr 23 '15 at 9:05

3 Answers
3

I personally recommend WPS Office. It isn't just a PDF viewer. As the name implies it supports Word, Excel and Power point documents as well. It is really fast in rendering and you can open multiple documents at the same time and switch between the tabs. The only requirement that is not satisfied is small size. The app is approximately 30Mbs and reaches 90 mbs after installation. But trust me, the rendering speed is SUPERB.

The only problem is you have to clean the cache manually as the app can accumulate a lot of useless data (sometimes 1Gb if you don't clean for like a month). All you've gotta do is go to your device's app manager and tap clear cache.

It should meet, if not all, most of your listed needs:
it is the smallest PDF Viewer for Android and the less permission asking I've ever used. It doesn't require internet access to work, in terms of size it should stay in the 10MB (thus if you decide to move it to SD size becomes a little bigger), I find it's fast, it's free and I didn't noticed ads (if they are there they are really non intrusive as I never remember seeing one).
Finally, it has night mode (color switching) and it is not made by Google or Adobe.